Parrikar told reporters that Reddy's resignation has been accepted.
His appointment was challenged in the High Court by social activist Aires Rodrigues which was dismissed.
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"He has pointed out that he wants to resign on personal grounds. We have accepted the resignation," the CM said.
Reddy, the first ever Lokayukta of the state, assumed charge in March 2013. His office was situated at Altinho in Panaji.
The Lokayukta is currently hearing various cases, including the multi-crore illegal mining scam.